Bounds on Codes Derived by Counting Components in Varshamov Graphs

We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10]     

Geometry optimised AB initio calculations on cyclopropenone and dimethylcyclopropenone adducts with borane and trifluoroborane

Geometry optimised ab initio calculations are reported for R₂C₃O.BY₃ (R = H, CH₃; Y = H, F). The results show that in the above series BH₃ is a stronger Lewis acid than BF₃, and that dimethylation increases the basicity of the cyclopropenone system.     

Inactivation of nitroalkane oxidase upon mutation of the active site base and rescue with a deprotonated substrate

Mutation of Asp402 in nitroalkane oxidase to Asn or Ala inactivates the enzyme with neutral nitroethane as substrate, but the activity can be rescued with the nitroethane anion. The V/K values of the D402N and D402A enzymes with the nitroethane anion are independent of pH, whereas the V/K values of the wild-type and D402E enzymes are pH dependent with both the protonated and the deprotonated forms of nitroethane. Moreover, although the V/K value of the D402E enzyme with neutral nitroethane is 20-fold less than that of the wild-type enzyme, there is only a 2-fold difference in the V/K values with the nitroethane anion. These results are fully consistent with a primary role for Asp402 as the active site base in nitroalkane oxidase which abstracts the substrate alpha-proton.     

The chemistry of cyclic enaminoketones. III. Synthesis of bi- and tricyclic enaminoketones from enamine esters and nitriles

The cyclization of enamines derived from β-aminoesters and β-aminonitriles into bi- and tricyclic enaminoketones ( 6,9,13 and 24 ) has been investigated. The enamines derived from aminonitriles cyclize smoothly with magnesium perchlorate in benzene or toluene, whereas the enamines derived from aminoesters cyclize spontaneously during their formation. The scope and limitation of this process is discussed.     

Deuterium isotope effect in (+)-glutamic acid hydrochloride

A study of the effects of deuterium substitution in (+)-glutamic acid hydrochloride is described. Solid state vibrational spectra depicting band shifts resulting from deuterium indicate that interatomic bond distances remain virtually unchanged. The cell volume expands only 0.05% upon deuteration, while the macroscopic linear and nonlinear polarizabilities are unaffected. The optical nonlinearity is therefore ascribed to the electronic nature of the hydrogen bonds.     

High‐pressure studies of the micro‐Raman spectra of iron cyanide complexes: Prussian blue (Fe4[Fe(CN)6]3), potassium ferricyanide (K3[Fe(CN)6]), and sodium nitroprusside (Na2[Fe(CN)5(NO)]·2H2O)

The pressure dependences of the peaks observed in the micro‐Raman spectra of Prussian blue (Fe₄[Fe(CN)₆]₃), potassium ferricyanide (K₃[Fe(CN)₆]), and sodium nitroprusside (Na₂[Fe(CN)₅(NO)]·2H₂O) have been measured up to 5.0 GPa. The vibrational modes of Prussian blue appearing at 201 and 365 cm⁻¹ show negative dν/dP values and Grüneisen parameters and are assigned to the transverse bending modes of the Fe C N Fe linkage which can contribute to a negative thermal expansion behavior. A phase transition occurring between 2.0 and 2.8 GPa in potassium ferricyanide is shown by changes in the spectral region 150–700 cm⁻¹. In the spectra of the nitroprusside ion, there are strong interactions between the FeN stretching mode and the FeNO bending and the axial CN stretching modes. The pressure dependence of the NO stretching vibration is positive, 5.6 cm⁻¹ GPa⁻¹, in contrast to the negative behavior in the iron(II)‐meso‐tetraphenyl porphyrinate complex. Copyright © 2011 John Wiley & Sons, Ltd.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

Geometry optimised ab initio calculations on cyclopropenone and dimethylcyclopropenone

Geometry optimised ab initio calculations are reported for cyclopropenone (I) and its dimethyl derivative (II). The effect of the methyl substituents in this strained ring system with an exocyclic heteroatom is to increase the bond lengths and the electronic delocalisation. For cyclopropenone the results are compared, firstly, with previous ab initio calculations, without geometry optimisation, secondly, with a semi-empirical calculation with partial optimisation, and finally, with experimental results. The calculated geometry for this molecule agrees with the experimental results.